WEBVTT

1
00:00:00.000 --> 00:00:04.447
Here is the problem: |3x minus 2| less than or equal to 7.

2
00:00:04.897 --> 00:00:12.420
Solve an absolute value inequality by turning it into a compound inequality and finding the boundary points.

3
00:00:13.220 --> 00:00:22.055
Write the problem with the absolute value isolated. The absolute value is already alone on one side, so it can be split into cases.

4
00:00:22.505 --> 00:00:27.776
Rewrite as a compound ("and") inequality. The inside must lie within c units of zero.

5
00:00:28.226 --> 00:00:34.077
Find the endpoints by solving each boundary equation. The solution lies between the endpoints.

6
00:00:34.527 --> 00:00:37.232
Write the solution set in interval notation.

7
00:00:38.032 --> 00:00:46.217
So the answer is negative 5 over 3 less than or equal to x less than or equal to 3; interval notation: [-5 over 3, 3].

8
00:00:46.667 --> 00:00:57.348
An absolute value inequality compares a distance with c: "less than" keeps the inside within c of zero (one interval), "greater than" pushes it beyond c (two rays).

9
00:00:58.148 --> 00:01:08.237
Test point x equals 2 over 3 (midpoint): |0| equals 0 less than or equal to 7, so the inside of the interval satisfies the inequality.